Exercise 1 Page P10

Before we consider the given number, let's recall the various types of numbers.

• Rational Number: A number is a rational number if it can be written in the form ab, where a and b are both integers and b≠ 0.
• Integer: A number is an integer if it is a positive or negative counting number (or zero). All integers are also rational numbers because any number can be written as a division by one, a1.

• Whole Number: A number is a whole number if it is a non-negative counting number. All whole numbers are also integers and rational numbers.
  
  • Natural Number: A number is a natural number if it is a positive counting number. All natural numbers are also whole numbers, integers, and rational numbers.
  
  • Irrational Number: An irrational number is a number that cannot be written in the form of a rational number. These are recognized as being non-repeating, infinite decimals.

  Now, let's try to categorize the given number using these definitions. -sqrt(64) It looks like it is possible to simplify this radical number, so let's do that before we classify it.

  -sqrt(64)

  SplitIntoFactors

  Split into factors

  -sqrt(8* 8)

  WritePow

  Write as a power

  -sqrt(8^2)

  SqrtPowToNumber

  sqrt(a^2)=a

  -8

  After simplifying, we were left with a negative counting number. Therefore, it is an integer and rational number.